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The maximum number of equivalence relations on the set A = {1, 2, 3} are

 The maximum number of equivalence relations on the set A = {1, 2, 3} are

Grade:12

1 Answers

Harshit Singh
askIITians Faculty 5968 Points
11 months ago
Dear Student

The correct answer is 5
Given that,
set A = {1, 2, 3}
Now, the number of equivalence relations as follows
R1= {(1, 1), (2, 2), (3, 3)}
R2= {(1, 1), (2, 2), (3, 3), (1, 2), (2, 1)}
R3= {(1, 1), (2, 2), (3, 3), (1, 3), (3, 1)}
R4= {(1, 1), (2, 2), (3, 3), (2, 3), (3, 2)}
R5={(1,2,3)⇔AxA=A^2}
Hence, maximum number of equivalence relation is ‘5’.

Thanks

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